Abstract:
Scaling models of geofields attempt to capture the strong and wide-range variability ubiquitous in geosystems. Unfortunately, they are generally both isotropic (self-similar) and monofractal (non-intermittent, quasi-Gaussian). In this first paper of a two-paper series, we lift the first of these restrictions, arguing that anisotropic scaling is essential for taking into account the stratification of the Earth and its consequences. In particular, at horizontal scales below several thousand kilometres we model the thin or Curie-depth-limited crustal magnetization and the corresponding surface magnetic field (B) by using anisotropic scaling. We show that it generically gives rise to a new intermediate scaling (`red noise') surface B field regime quantitatively very close to that observed on two sets of regional surface B field surveys. This scaling is impossible to explain using standard self-similar models. Using these data as well as horizontal and vertical susceptibility data, we estimate the basic model parameters and show that that model is compatible with the available data. In Paper II we lift the monofractal restriction and perform multifractal analyses; we then extend the anisotropic scaling model to include multifractal B and magnetization fields.
